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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.
Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m (round off to the nearest integer).
Correct answer is between '104,106'. Can you explain this answer?
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The barrier shown between two water tanks of unit width (1 m) into the...
Concept:
Net hydrostatic force exerted by fluid on flat surface, F = ρ × g × h̅ × A
Where, ρ = density of fluid, g = acceleration due to gravity, A = Area of the flat surface, h̅ = depth of centroid from free surface
This force is assumed to be acting at a point.
Centre of the pressure of rectangular lamina from free surface,
CP = 2/3h (h = height of rectangular lamina)
Calculation:
For left side of the barrier
Area = 4 m × 1 m = 4 m2, h¯= 4 / 2 = 2m,
Center of pressure from top surface of the water, CP1 = 2 × 4 / 3 = 8 / 3m
F1= ρ × g × h̅ × A = 1000 × 10 × 2 × 4 = 80 kN
For right side of the barrier
Area = 1 m × 1 m, h¯= 1 / 2 = 0.5m,
Center of pressure from top surface of the water CP2 = 2 × 1 / 3 = 2 / 3m
F2 = ρ × g × h̅ × A = 1000 × 10 × (1 × 1) × 0.5 = 5 kN
Distance of centre of pressure from bottom end:
CP1 = h/3 = 4/3
CP2 = h/3 = 1/3
These forces will act as point load on the barrier. If the barrier is treated as a cantilever and the fixed end of this cantilever beam is on the bottom side of the tank, then the loading conditions will look like the figure drawn below
F1 = 80 kN, F2 = 5 kN
From the above-simplified diagram:
A moment about the fixed end of barrier,
Net hydrostatic force exerted by fluid on flat surface, F = ρ × g × h̅ × A
Where, ρ = density of fluid, g = acceleration due to gravity, A = Area of the flat surface, h̅ = depth of centroid from free surface
This force is assumed to be acting at a point.
Centre of the pressure of rectangular lamina from free surface,
CP = 2/3h (h = height of rectangular lamina)
Calculation:
For left side of the barrier
Area = 4 m × 1 m = 4 m2, h¯= 4 / 2 = 2m,
Center of pressure from top surface of the water, CP1 = 2 × 4 / 3 = 8 / 3m
F1= ρ × g × h̅ × A = 1000 × 10 × 2 × 4 = 80 kN
For right side of the barrier
Area = 1 m × 1 m, h¯= 1 / 2 = 0.5m,
Center of pressure from top surface of the water CP2 = 2 × 1 / 3 = 2 / 3m
F2 = ρ × g × h̅ × A = 1000 × 10 × (1 × 1) × 0.5 = 5 kN
Distance of centre of pressure from bottom end:
CP1 = h/3 = 4/3
CP2 = h/3 = 1/3
These forces will act as point load on the barrier. If the barrier is treated as a cantilever and the fixed end of this cantilever beam is on the bottom side of the tank, then the loading conditions will look like the figure drawn below
F1 = 80 kN, F2 = 5 kN
From the above-simplified diagram:
A moment about the fixed end of barrier,
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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. Can you explain this answer?
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